Dollar Shave Club, which is basically just razors sold through the mail, sold for $1 billion. The subscription razor delivery service offers its wholesale-cost shaving products for anyone who wants to use them—but it's still mostly marketed for men.

That's why the founders of Billie, a new startup, think they have a way into the surprisingly lucrative subscription shaving business.

"We looked at the shaving categories and we saw a lot of companies focused on providing a better shaving experience for men," co-founder Georgina Gooley said. "Women have been kind of an afterthought in this category."

Even if women can technically subscribe to a shaving box and use men's razors and shaving cream, Gooley and her co-founder Jason Bravman think that shouldn't be the only option. What about women who want a pink razor or one that has soap around the edges? Or want shaving cream that isn't trying to be so manly?

And what if women don't want to pay more for products that more directly address them?

Billie subscribers pay $9 and get a razor handle, a magnetic razor holder, and two razor cartridges. After that, each $9 refill comes with four razor cartridges. Subscribers choose whether they want a refill every one, two, or three months. Billie also offers supplemental products, including an $8 shave cream, a $9 body wash, and a $12 body lotion.

The prices are important because in addition to offering a subscription model that's totally focused on women, Billie is determined to counter the pink tax, or the extra few cents or dollars women often pay for products just because they're the women's version. Its razors are priced similarly to Dollar Shave Club's, where a starter set is $5 and refills cost $9 a month, and are about half the price of similar drugstore women's razors.

As part of its marketing promo, the startup is offering a "pink tax rebate," or a Billie credit for sharing referral codes with friends. But besides the marketing gimmick, Billie is committed to providing an affordable alternative in a corner of the subscription craze that has pretty much ignored women so far.

The founders are prepared to compete in an industry that's produced billion-dollar acquisitions. They've raised an undisclosed amount of funding led by Sherpa Capital, which has invested in Uber and Airbnb. Bravman's brother-in-law is Warby Parker co-founder Neil Blumenthal, and his sister Rachel Blumenthal founded the kids' clothing startup Rockets of Awesome. Gooley came from the advertising world, where she worked on campaigns for Old Spice.

They're following a proven business model, but with a different focus.

"When we look at what's going on with women, we see startups created for men first swap some hot pink on the product and say it's for women," Bravman said. "For us, we wanted to create a company that really puts women first and acknowledges women are equally frustrated with the price of razors, if not more."

As for their billion-dollar competitor?

"Those guys have created such a strong brand and following amongst their male audience base. They have a lot more guys they can go after in that category," Gooley said. "They're doing it really well and they should stay focused on that."